When solving trigonometric expressions like sine, cosine and
tangent, it is very important to realize that Excel uses radians,
not degrees to perform these calculations! If the angle is in
degrees you must first convert it to radians.

Recall that p
= 180°. Therefore, if the angle is in degrees, multiply it by
p/180°
to convert it to radians. With Excel, this conversion can be
written PI( )/180. For example, to convert 45° to
radians, the Excel expression would be 45*PI( )/180 which equals
0.7854 radians.

Excel has a built-in function known as RADIANS(angle)
where angle is the angle in degrees you wish to convert
to radians. For example, the Excel expression used to convert
270° to radians would be RADIANS(270) which equals 4.712389
radians

You
can use the DEGREES(angle) function to convert radians into
degrees. For example, DEGREES(PI( ) ) equals 180.

Excel uses several built-in trig functions. Those that you will use
most often are displayed in the table below. Note that the
arguements for the SIN( ), COS( ) and TAN( ) functions are,
by default, radians. Also, the functions ASIN( ), ACOS( )
and ATAN( ) return values in terms of radians. (When
working with degrees, you will need to properly use the DEGREES( )
and RADIANS( ) functions to convert to the correct unit.)

Mathematical
Expression

Excel
Expression

Excel Examples

sine: sin(q)

SIN(number)

SIN(30) equals -0.98803, the sine of 30 radians

SIN(RADIANS(30)) equals 0.5, the sine of 30°

cosine: cos(q)

COS(number)

COS(1.5) equals 0.07074, the cosine of 1.5 radians

COS(RADIANS(1.5)) equals 0.99966, the sine of 1.5°

tangent: tan(q)

TAN(number)

TAN(2) equals -2.18504, the tangent of 2 radians

TAN(RADIANS(2)) equals 0.03492, the tangent of 2°

arcsine: sin-1(x)

ASIN(number)

ASIN(0.5) equals 0.523599 radians

DEGREES(ASIN(0.5)) equals 30°, the arcsine of 0.5

arccos: cos-1(x)

ACOS(number)

ACOS(-0.5) equals 2.09440 radians

DEGREES(ACOS(-0.5)) equals 120°, the arccosine of -0.5

arctangent: tan-1(x)

ATAN(number)

ATAN(1) equals 0.785398 radians

DEGREES(ATAN(1)) equals 45°, the arctangent of 1

Below are a few examples of problems involving trigonometry and how
we used Excel to help solve them.

Say, for instance, we want to know the height of the tree in the
figure shown above. We know that if we stand 76 m from the base of
the tree (x = 76 m) the line of sight to the top of the tree
is 32° with respect to the horizon (q
= 32°). We know that

Solving for the height of the tree, h, we find .
The screen shot below shows how we used Excel to determine that the
height of the tree is 47 m.

Note
the use of the RADIANS( ) function in the above example.

In this next example, we wish to know the launch angle, a,
of the water ski ramp pictured above. We are given that A = 3.5 m, B
= 10.2 m and b
= 45.0°. To find a,
we can use the Law of Sines which, in this case can be
written

We can rewrite this equation as .
Using the arcsine (inverse sine) we can find the angle a
using the equation

The screen shot below shows how we used Excel to determine that the
launch angle of the ramp is 14.04°.

Note
the use of the DEGREES( ) and RADIANS( ) function in the above
example.

In our final trigonometry example, we will use Excel to examine the
trig identity

Notice in the screen shot below that this identity holds true when
q
is given in radians and degrees.

Note
the units for the angle q
are placed in different cells than the numbers. If we place the
numbers and the units in the same cell, Excel will not be able to
decipher the number and therefore we will not be able to reference
the cells for use in any equation!